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Hello, I was hoping you could help me verify this identity. I'm actually really good at the various identities and verifying them, but this problem is proving really complex for me and I just can't seem to get through it. I was hoping you could really show me step-by-step on how to get the answer for this problem.

It is:
((cos(a)-cos(b))/(sin(a)+sin(b)))+((sin(a)-sin(b))/(cos(a)+cos(b)))= 0

I created an image of it for you here, might be easier to work with visually:

Thank you for your help in advance, I appreciate you taking the time to assist.

You have:

cos(a)-cos(b)      sin(a)-sin(b)
--------------- +  -------------
sin(a)+sin(b)      cos(a)+cos(b)

How about combining?  [Note abbreviations]

(ca-cb)(ca+cb) + (sa-sb)(sa+sb)

ca^2-cb^2 + sa^2-sb^2
[  etc  ]

ca^2 + sa^2 - sb^2 - cb^2
[  etc  ]

ca^2 + sa^2 - (sb^2 + cb^2)
[  etc  ]

Now a little trig should finish it for you.  

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Paul Klarreich


I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.


I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.


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